SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.6. POLAR MATERIALS AND STRUCTURES 391

n-GaN Substrate

+Qπ

-Qπ

EF

EC

EV

+eNDD

(b)

Defective

region

Ionized

surface states

+

+

+

+

+

+

+

+

-eNDD+

EDD

n-GaN Substrate

+Qπ

-Qπ

EF

EC

EV

(a)

Defective

region

EDD

Figure 8.20: Schematic diagram of ann-type GaN sample along with charge profile and band
diagram when the effects of surface states are taken into account. (a) Very thin GaN, for which
surface states are not ionized. (b) Once GaN is thick enough such thatEDDis very close toEF
at the GaN surface, surface donors become ionized and polarization charge is screened.

depth(EC−EDD)/e, as illustrated in figure 8.20. As the epitaxial thickness increases, the
donor levelEDDapproaches the Fermi levelEFat the GaN surface, and the screening charge
NDD+ increases as given by the Fermi-Dirac occupancy probability

NDD+ =[1−f(EDD(0))]NDD (8.6.6)

=

⎡

⎣

exp

(

EDD(0)−EF

kBT

)

1+exp

(E

DD(0)−EF

kBT

)

⎤

⎦·NDD (8.6.7)